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satisfying Write a matrix for the linear transformation T: R³ R³ ¹ () - () · () - () · ¹) - () T = T = 2 TO = 5 0 1 2 4

satisfying Write a matrix for the linear transformation T: R³ R³ ¹ () - () · () - () · ¹) - () T = T = 2 TO = 5 0 1 2 4

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 34E
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**Problem Statement:** Write a matrix for the linear transformation \(T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) satisfying: \[ T \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = \begin{pmatrix} 2 \\ 1 \\ 5 \end{pmatrix} ,\quad T \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix} ,\quad T \begin{pmatrix} 0 \\ 0 \\ 2 \end{pmatrix} = \begin{pmatrix} 0 \\ 2 \\ 4 \end{pmatrix}. \]
Transcribed Image Text:**Problem Statement:** Write a matrix for the linear transformation \(T : \mathbb{R}^3 \rightarrow \mathbb{R}^3 \) satisfying: \[ T \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = \begin{pmatrix} 2 \\ 1 \\ 5 \end{pmatrix} ,\quad T \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix} ,\quad T \begin{pmatrix} 0 \\ 0 \\ 2 \end{pmatrix} = \begin{pmatrix} 0 \\ 2 \\ 4 \end{pmatrix}. \]
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